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Algorithms and Proofs Inheritance in the FOC Language

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Abstract

In this paper, we present the FOC langugage, dedicated to the development of certified computer algebra libraries (that is sets of programs). These libraries are based on a hierarchy of implementations of mathematical structures. After presenting the core set of features of our language, we describe the static analyses, which reject inconsistent programs. We then show how we translate FOC definitions into OCAML and COQ, our target languages for the computational part and the proof checking, respectively.

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References

  1. Ballarin, C., Homann, K. and Calmet, J.: Theorems and algorithms: An interface between Isabelle and Maple, in A. Levelt (ed.), Proceedings of ISSAC, Montréal, Canada, ACM Press, 1995, pp. 150–157.

    Google Scholar 

  2. Betarte, G.: Dependent record types and formal abstract reasoning: Theory and practice, Ph.D. thesis, University of Göteborg, 1998.

  3. Boulmé, S., Hardin, T. and Rioboo, R.: Polymorphic data types, objects, modules and functors: Is it too much? Research Report 14, LIP6, 2000. Available at http://www.lip6.fr/reports/ lip6.2000.014.html.

  4. Boulmé, S., Hardin, T. and Rioboo, R.: Some hints for polynomials in the FOC project, in Calculemus 2001 Proceedings, June 2001.

  5. Boulmé, S.: Spécification d'un environnement dédié à la programmation certifiée de bibliothèques de Calcul Formel, Ph.D. thesis, Université Paris 6, 2000.

  6. Buchberger, B. et al.: A survey on the Theorema project, in W. Kuechlin (ed.), Proceedings of ISSAC'97, ACM Press, 1997.

  7. Cerioli, M., Mosses, P. and Reggio, G. (eds): Proceedings of the 15th International Workshop on Algebraic Development Techniques and the General Workshop of the CoFI WG, Genova, Italy, April 2001.

  8. Dalmas, S., Gaëtano, M. and Watt, S.: An OpenMath 1.0 implementation, in W. Kuechlin (ed.), Proceedings of ISSAC'97, ACM Press, 1997.

  9. Davenport, J., Siret, Y., Tournier, E. and Lazard, D.: Computer Algebra, Masson, 1993.

  10. Dunstan, M., Gottliebsen, H., Kelsey, T. and Martin, U.: Computer algebra meets automated theorem proving: A Maple-PVS interface, in Proceedings of the Calculemus Workshop, 2001.

  11. Farmer, W. M., Guttman, J. D. and Thayer, F. J.: The IMPS user's manual, Technical Report M-93B138. The MITRE Corporation, November 1995. Available at ftp:// math.harvard.edu/imps/doc/.

  12. Fechter, S.: Une Sémantique pour FOC, Rapport de D.E.A., Université Paris 6, Septembre 2001.

  13. Geuvers, H., Pollack, R., Wiedijk, F. and Zwanenburg, J.: The algebraic hierarchy of the FTA project, in Proceedings of the Calculemus Workshop, 2001.

  14. Harrison, J. and Théry, L.: A skeptic's approach to combining HOL and Maple, J. Automated Reasoning 21 (1998), 279–294.

    Google Scholar 

  15. Jackson, P.: Exploring abstract algebra in constructive type theory, in Proceedings of 12th International Conference on Automated Deduction, 1994.

  16. Jenks, R. D. and Stutor, R. S.: AXIOM, The Scientific Computation System, Springer-Verlag, 1992.

  17. Leroy, X., Doligez, D., Garrigue, J., Rémy, D. and Vouillon, J.: The Objective Caml system release 3.00 Documentation and user's manual, INRIA, 2000. http://pauillac.inria.fr/ ocaml/htmlman/.

  18. Mandel, L.: Factorisation de polynômes sur les corps finis, Rapport de magistére, Université Paris 6, 2001.

  19. Pollack, R.: Dependently typed records for representing mathematical structures, in TPHOLs'00, Springer-Verlag, 2000.

  20. Pottier, L.: Contrib. algebra. http://coq.inria.fr/contribs-eng.html.

  21. Prevosto, V.: Vers une interface utilisateur pour foc, Rapport de D.E.A., Université Paris 6, Septembre 2000.

  22. Prevosto, V. and Doligez, D.: Algorithms and proofs inheritance in the FOC language, Research Report, LIP6, 2002 (to appear). Available at http://www-spi.lip6.fr/~prevosto/ papiers/rr02.ps.gz.

  23. The Coq Development Team: The Coq Proof Assistant Reference Manual, Projet LogiCal, INRIA-Rocquencourt – LRI Paris 11, Nov. 1996.

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Prevosto, V., Doligez, D. Algorithms and Proofs Inheritance in the FOC Language. Journal of Automated Reasoning 29, 337–363 (2002). https://doi.org/10.1023/A:1021979218446

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